Abstract

Let $p$ be an odd prime number and $F$ a field containing a primitive $p$th root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group $G_F$ of $F$. Namely, the third subgroup $G_F^{(3)}$ in the descending $p$-central sequence of $G_F$ is the intersection of all open normal subgroups $N$ such that $G_F/N$ is $1$, ${\Bbb Z}/p^2$, or the extra-special group $M_{p^3}$ of order $p^3$ and exponent $p^2$.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1503-1532
Launched on MUSE
2011-12-01
Open Access
No
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